Conventionally, there has been known a carbon nanostructure including a linear structure in which carbon atoms are aligned in a nanometer-level diameter and a sheet-like structure constituted by carbon atoms and having a nanometer-level thickness, which are typified by carbon nanotube, graphene and the like. As a method for manufacturing such carbon nanostructure, there has been proposed a method for supplying a carbon-containing source gas to a heated fine catalyst, thereby growing a carbon nanostructure from the catalyst (refer to, for example, Japanese Patent Laying-Open No. 2005-330175).